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winograd minimal filtering for Convolutional Neural Network

I'm going to use the Winograd’s minimal filtering algorithms to introduce a new class of fast algorithms for convolutional neural networks using C and OpenBLAS. It is a first implementation of the Fast Algorithms for Convolutional Neural Networks - Paper

Theoretical Background

The algorithm that we are going to implement relize the operation in the image below.

We have extended the algorithm by using more dimension: <br/> Image

• W x H x Channel -> It can be seen as a cube with a width, an height and a number of channels
• In our implementation we consider W = H <br/>Kernel
• R x R x Channel x K -> It can be seen as a "list of cube". We have K cubes with a dimension of R x R x Channel <br/>Tile
• A tile is a "Portion of the image" with a dimension D X D x Channel.
• The only requirement that we have is that D should be divisor of W (and H)
• We can consider (W / D) * (W / D) different tiles in a single image. <br/>Output
• The output of a tile is a matrix of a dimension of M x M
• The program will give us as an output a cube with a dimension of M * (W / D) x M * (W / D) x K
• By using a tensorflow notation a single output tile is calculated as: <br/>output[k,h,w] = sum_{c,dh,dw} input[c, h + dh, w + dw] * filter[k,c,h,k] <br/>but instead of using this formula we have implemented it with the winograd algorithm.

Parameters

• M - dimension of an output tile
• R - dimension of the kernel
• Channel - number of channel of the image and of the kernel
• K - number of kernels
• W - width of the image
• H - height of the image
• kernel.txt - file of the input kernel
• input.txt - file of the input image

Getting Started

These instructions allow you to run the program on your computer.

Prerequisites

• Install openBlas on your computer
• Install python with np on your computer

Installing

We need to compile the program, you should give to the compiler the path of the openBLAS library. I use this line:

cc -static -o test main.c -I /opt/OpenBLAS/include/ -L/opt/OpenBLAS/lib -lopenblas -lpthread -lgfortran

Running an example

To run an example of the program you should follow these steps:

• Create the matrix parameters

python calcMc.py M R

• Create the input image

python createInput.py W H CHANNEL input.txt

• Create the input kernel

python createKernel.py R CHANNEL K kernel.txt

• Call the C executable program with the correct parameters

./test M R CHANNEL K W H kernel.txt input.txt

Contributing

This project has been developed by Me and Andrea Facchini